According to a celebrated theorem of Roger Penrose:

Theorem(Penrose 1965). Globally hyperbolic spacetimes satisfying the null energy condition and containing a closed trapped surface and a non-compact Cauchy hypersurface are necessarily future-causally geodesically incomplete.

The above is typically known as "Penrose's singularity theorem". In view of the precise statement of the thorem, it is perhaps less confusing to just refer to it as "Penrose's *incompleteness* theorem".

While the above theorem tells us that under very general initial conditions, something goes wrong, it does not tell us what.

Two fundamental quations that one can ask are: *Is this incompleteness seen by far away observers*, and, *does this incompleteness lead to a breakdown of the predictability of the theory*. These are related to the so-called weak and strong cosmic censorship conjectures.